Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
190 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #26011887 | C2 | semidirect |
| 3. #26011843 | C2 | semidirect |
| 6. C8×#13063436 | C2 | semidirect |
| 7. #487×C173 | C2 | semidirect |
| 68. C173 | #1708 | semidirect |
| 73. #487 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011887 | 2 |
| #26011865 | 2 |
| #26011843 | 2 |
| #26011839 | 2 |
| #26011838 | 2 |
| C8×#13063436 | 2 |
| #487×C173 | 2 |
| #1708 | 173 |